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In clinical study, calculation for sample size is often done using the frequentist framework. However, several methods of calculation using the Bayesian framework have been proposed. In this paper, we propose a method for the determination of sample sizes using the index 𝜃 = P 𝜋1 > 𝜋2 X1, X2 , where X1 and X2 denote the binomial random variables for trials n1 and n2 and parameters π1 and π2, respectively. In this paper, we propose a new method of calculation, by which we determine in advance the estimated difference between the posterior proportions and the value to be derived at the end of the test to obtain the necessary sample size. We provide the lists of necessary sample sizes with various assumptions and the calculation program using Mathematica.
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